Frequency bands for wireless communications have rapidly increased with diffusion of mobile phones in recent years. To use limited frequency resources effectively, a frequency interval (guard band) between a transmission band and a reception band assigned to a communication system becomes smaller. Moreover, a frequency interval between different communication systems also becomes smaller.
Such a circumstance requires a filter and a duplexer used in a wireless communication device such as a mobile phone terminal to reduce frequencies for switching from a pass band to a blocking band. That is to say, a filter and a duplexer are desired to have a steep cutoff characteristic. When an acoustic wave resonator is used for a filter or duplexer, a cutoff characteristic can be made steep by making an electromechanical coupling coefficient small as disclosed in Japanese Patent Application Publication No. 2002-319842. Moreover, a degree of suppression in a blocking band of the filter or duplexer is required to be high to prevent interference between a transmission signal and a reception signal, or interference between different communication systems.
When an acoustic wave resonator is used for a filter or duplexer, a cutoff characteristic can be made steep by making an electromechanical coupling coefficient small. However, there is a tradeoff relationship that a passband width becomes narrow as a cutoff characteristic becomes steep, and a cutoff characteristic is difficult to be made steep with maintaining the passband width. In addition, a degree of suppression in a blocking band is in a tradeoff relationship with a loss in a passband, and it is difficult to improve the degree of suppression in the blocking band with suppressing an increase in loss in the passband.